<h2>题目编号 : 204</h2>
<div style="color:#666;font-size:80%;">06 September 2008</div><br />
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<p>A Hamming number is a positive number which has no prime factor larger than 5.<br/>
So the first few Hamming numbers are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15.<br/>
There are 1105 Hamming numbers not exceeding 10<img src="" style="display:none;" alt="^(" /><sup>8</sup><img src="" style="display:none;" alt=")" />.</p>

<p>We will call a positive number a generalised Hamming number of type <var>n</var>, if it has no prime factor larger than <var>n</var>.<br/>
Hence the Hamming numbers are the generalised Hamming numbers of type 5.</p>

<p>How many generalised Hamming numbers of type 100 are there which don't exceed 10<img src="" style="display:none;" alt="^(" /><sup>9</sup><img src="" style="display:none;" alt=")" />?</p>
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